Bellman-Steffensen type inequalities

J Inequal Appl. 2018;2018(1):288. doi: 10.1186/s13660-018-1882-9. Epub 2018 Oct 22.


In this paper some Bellman-Steffensen type inequalities are generalized for positive measures. Using sublinearity of a class of convex functions and Jensen's inequality, nonnormalized versions of Steffensen's inequality are obtained. Further, linear functionals, from obtained Bellman-Steffensen type inequalities, are produced and their action on families of exponentially convex functions is studied.

Keywords: Bellman–Steffensen type inequality; Exponential convexity; Measure theory; Steffensen’s inequality.